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Density Functional Theory provides a powerful tool to study the electronic structure of complex materials. In this monograph, we employ DFT to study Topological Insulators, which are materials exhibiting a novel quantum state of matter. These materials have recently attracted a lot of attention in a vision to harness these unconventional properties into possible device applications based on the unique interplay between spin and charge. We also have used DFT to investigate overdoped high temperature cuprate superconductors, materials that have been the subject of intense research since their discovery two decades ago.